Accounting for Teammates Part 1: Corsi Rel and WOWY

Jared Lunsford
July 18 2012 05:56PM

 

 

The quality of teammates influences almost every stat in all major sports. This is particularly true of the base stats we tend to use, such as on-ice Corsi or Fenwick rate, because they don't just take something a player has done (score a goal) but also include what his teammates did while he was on the ice. The reason we opt for on-ice stats instead of individual is simple - on-ice stats allow us to measure, albeit noisily, all the contributions a player makes to the thing you are measuring.

How often do you hear an announcer say "that kind of play doesn't show up on the stat sheet, but was very important"? If you're measuring on-ice stats instead of individual stats, and you have a large enough sample, those small plays will show up. The trick is accounting for teammate quality, or at the very least taking it into consideration.

Challenges

The first thing one should recognize is that it's often difficult or even impossible to separate out guys that spend the majority of their time together. The Sedins are an obvious example, but it is very common for a top defense pairing to stick together most of a season and somewhat common for pairs or even entire lines of forwards to play the vast majority of their time together.

It all comes down to sample size. With apologies to Nashville fans in mourning, consider Shea Weber and Ryan Suter last season. Going by hockey analysis, at 5-on-5 they spent 1,293 minutes together, Suter played just under 213 minutes without Weber and Weber played almost 195 minutes without Suter. So they each played roughly 3 games' worth of time apart. With a sample size that small, we can't say much of anything.

Any team can look good or terrible over a three-game stretch. Last year Weber did substantially better when they were apart, but to figure out if one was driving play more than the other you would need several seasons' worth of data and even then it's just going to be a rough idea because those two spent so much of their time together.

A First Attempt - Relative Corsi

The most well known and, unfortunately, most widely used method of dealing with teammates is relative Corsi (Corsi Rel). To calculate relative Corsi, you simply take the possession rate when the player is on the ice and subtract off the possession rate when he is off the ice. The idea, broadly speaking, is that if a player is helping his team then, they will be better off with him on the ice than off. That's a fine idea but I have to say I'm not a fan of this metric at all. I'd love for someone to defend it in the comments because it puzzles me that it is ubiquitous given its major flaws. My intuition is that zone-start adjusted Corsi and maybe even just raw Corsi are better metrics than Corsi Rel.

Fellow Driving Play and NHLnumbers blogger Brent Morris provided a nice article of criticisms. In fairness, one could argue that a lot of the problems are down to misuse. Corsi Rel doesn't really adjust for teammates so much as say how your line/pairing does compare to the others on your team. The adjustment, subtracting off the team's Corsi when you are off the ice, puts most of the weight on the guys the player in question never plays with. If you are a first-pairing defensemen, it's mostly going to be determined by how well the second and third pairings go.

What we'd like to do is see how much credit we should give a player versus the teammates he plays with, and Corsi Rel does that very poorly.

A Step Up - WOWY

WOWY, an acronym of "with or without you", is a pretty substantial improvement. In the basic version, one compares how each teammate does with a player on the ice to his results without that player. The idea is the same - if you are good, you will make your teammates better. If a guy is improving his line/pairing then the other player(s) will be better with him than without him.

WOWY adjusts for teammates (or teammate at least) by holding them constant. If you look at Crosby's performance with and without Pascal Dupuis, Crosby will appear on each side of that. This is a big improvement on Corsi Rel because if Dupuis spends a lot of time with Crosby, Sid would mostly be in the Corsi On part which would elevate Dupuis's numbers.

One big issue with WOWY is that you can still get a dragged-along-by-teammate effect if you aren't careful. If you look at a Vancouver defenseman's Corsi with and without Alex Burrows he will be drastically better with Burrows on the ice. Burrows may be a good possession player but as pointed out above it's tough to say since he spent so much time with the Sedins; so it seems likely that a healthy share of the credit there should go to Henrik and Daniel. For this reason it is generally best to run WOWY numbers against teammates on the same color line - forwards with forwards and defensemen with defensemen. If you run it on a defenseman for a forward or vice-versa the results will be very similar to Corsi Rel and carry all those problems.

It's beyond the scope of this article, but you can do more fancy versions of WOWY by looking at combinations of players. For example, you could look at Pittsburgh's Corsi rate with and without Dupuis when both Crosby and Letang were on the ice. This allows you to take into account the quality of both forward and defensemen. The downside is that you are going to shrink the sample sizes pretty dramatically so you might have to go to multiple seasons, which can cause its own problems.

Final Thoughts

Something to keep in mind with both of these is that you are always doing a comparison - in the case of Corsi Rel you are comparing a player, and his line, to the performance of his teammates when he is off the ice. If you have two equally skilled fourth liners, the one playing for Detroit or St. Louis will have a much worse Corsi Rel than the one playing in Minnesota or Nashville because the players in the comparison group are much better.

WOWY is the same way - Crosby's results without Dupuis depend on who tends to slot in when Dupuis is injured or shifted to another line. Keep in mind that you are always comparing a player's performance to some specific group of teammates. This is important if his team is very strong or weak at the same position or if you are using one of these to compare players on different teams.

In the next installment, I will look at a couple methods that get around this by assessing everyone at once - regression and Vic Ferrari's King Value.

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#1 Daniel Wagner
July 18 2012, 06:08PM
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I've never used Corsi Rel to account for teammates. I've mainly used it to compare between players on different teams. That way, a good player on a poor possession team can be (slightly) more accurately compared to a good player on a good possession team.

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#2 Eric T.
July 18 2012, 06:25PM
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Very nice, looking forward to part 2.

"If you are a first-pairing defensemen, it's mostly going to be determined by how well the second and third pairings go."

It's true that the difference between the first-pairing defenseman's Corsi and his Corsi Rel will be how the second and third pairings did. That means you're removing the effects of how good the team's forwards are, but adding in effects of how good the other defense pairings are. A priori, I wouldn't be able to say whether one is better than the other, but the fact that there's a little better heterogeneity across teams in the Corsi Rel leaders makes me feel warmer and fuzzier.

Either way though, it's definitely true that a 52% Corsi is a lot easier to achieve on a good team than on a bad one, and a +2% Corsi Rel is a lot easier to achieve on the top line of a bad team than on the top line of a good team. Which suggests both approaches have their weaknesses, and neither fully corrects for teammates.

WOWY has issues beyond the tag-along effect you describe. Much like with Corsi Rel, there's a big factor from how deep the lineup is. It's a lot easier for Mikko Koivu to appear to improve his linemates or the defensemen, since when they're not with him, they're with some random replacement-level guy. Re-reading, I guess you mention that in the conclusion, but I think it's a bigger problem than the one you focused on in the WOWY section.

My personal approach, for what it's worth, is to use Corsi Rel but keep the quality of the team in mind. "He had a neutral Corsi Rel in a very deep forward group" or "he was a slight minus in a weak forward group", for example.

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#3 Chris
July 18 2012, 06:27PM
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One good example against the relevance of relative corsi is the Canucks. The Sedins raw Corsi is about the same as their relative. Then Malhotra has a relative Corsi of -33, while his raw Corsi is actually -21, because he never plays with the Sedins.

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#4 Tach
July 18 2012, 06:33PM
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Thank you, thank you, thank you. I have long been critical of CorsiRel as a stat of any material use. The party line I had received was a player's possession was influenced by the possession rate of the team when he was off the ice.

I ran the R-squared on CorsiOn v CorsiOff for players with 20+GP in any season from 2009-10, 2010-2011 and 2011-2012 and only got ~.15. If a player's results were highly influenced by team results this seems pretty low, and certainly well below the level where they should each be rated 50/50.

I also ran r-squared for CorsiOn v (GF/60-GA/60) and CorsiRel v the same and CorsiOn has a higher correlation with Goal differential. This would indicate to me that CorsiOn better correlates with results, so it would seem a better predictor of ultimate results than CorsiRel.

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#5 Eric T.
July 18 2012, 06:46PM
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@Tach

Of course Corsi On correlates better with goal differential than Corsi Rel does -- there's no reason that subtracting out the team's results with you off the ice would improve the assessment of how the team does with you on the ice.

But it could improve the assessment of how much you individually contributed to those team results.

Imagine we had a direct measure of how much you drove possession, and found you were a +2% player. If you were playing with 55% linemates, both your 57% Corsi and your +2% True Talent would be good predictors of your results. But if you were playing with 45% linemates, your 47% Corsi would be a much better predictor of your results than the +2% True Talent would be. That doesn't mean it's a better assessment of your individual contribution.

I'm not saying Corsi Rel is that perfect measure, just that this correlation doesn't show what you're suggesting.

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#6 Eric T.
July 18 2012, 07:01PM
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@Tach

And incidentally, .15 sounds pretty high to me.

The average player with 20+ games played was on the ice for about 780 Corsi for events and 780 Corsi against events in 850 minutes. So the standard error on each of those counting statistics is sqrt(780) = 28, which means random chance should account for fluctuations in Corsi On of roughly +/- 3 shots per 60 minutes, or roughly 1/3 of the variance in Corsi On for that group. If your regression is correct, then the player's individual skill accounts for about half of the variance and the off-ice teammate skill accounts for about 1/6.

A correction factor that's 1/3 as important as the player's individual skill is actually pretty significant.

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#10 Andrew
July 18 2012, 09:13PM
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I agree with a lot of the RelCorsi criticisms, though WOWY seems to have similar problems, assuming I'm not wildly off base here. Take Suter and Weber again as examples. This year Suter performed worse when apart from Weber and Weber performed better without Suter, however this says nothing of the quality of teammates each played with when apart. Obviously, the difference in this case would likely be negligible, but in other cases it could be substantial.

Take a different example--Datsyuk and Zetterberg, who played a lot more time apart than together this past season. (Zetterberg was primarily paired with Filppula and Hudler, whereas Datsyuk was paired with Franzen and Bertuzzi.) They both did fantastic together, but apart it appears Datsyuk performed better than Zetterberg. (This passes the common sense test, at least.) However, Datsyuk also played with better teammates. Datsyuk played significantly more time with Lidstrom and White, and he wasn't saddled down with Filppula--who is consistently a minus possession player--or the disastrous pairing of Stuart and Kronwall on the blueline.

I dunno, like I said I could be wildly off base here, but I think it works best when comparing not just players of the same color line but players that played a significant amount of time together as well.

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#11 David Johnson
July 18 2012, 09:24PM
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@Jared Lunsford

I remember having this same debate with someone a few years ago but the player we debated about then was Kris Draper. I don't recall who I was debating but he claimed Draper was one of the worst players in the NHL because he was so bad relative to his teammates. Of course, his teammates at the time was a stacked team which made Draper look a lot worse than he was.

Teams like Vancouver, and Detroit of a few years ago, that rarely juggle lines and have a lot of top end talent make accounting for quality of line mates very difficult.

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#12 David Johnson
July 18 2012, 10:13PM
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@Andrew

"However, Datsyuk also played with better teammates."

I am not sure this is the case. I calculate TMCorF% (team mate corsi for percentage) which is the weighted average (weighted by TOI with) of each players teammates corsi for % when they are not playing with the player in question.

So, for Datsyuk if you take all of his teammates "without Datsyuk" corsi for% and take a weighted average weighted by TOI with Datsyuk you come up with 0.522. For Zetterberg, his TMCorF% is 0.530 (See http://stats.hockeyanalysis.com/ratings.php?disp=1&db=201112&sit=f10&pos=forwards&minutes=500&teamid=11&type=corsi&sort=PCT&sortdir=DESC). This means Zetterberg's team mates were better at controlling play when not playing with Zetterberg than Datsyuk's team mates were when they were not playing with Datsyuk.

Now, part of this might be Zetterberg playing with better line mates, but part of it might mean that when Zetterberg's line mates were not playing with him they were playing with Datsyuk and Datsyuk is a better player who positively influenced their stats.

But, that isn't necessarily a negative tick against TMCorF%. If teammates perform better with someone else, that should count as a negative towards Zetterberg relative to that someone else (Datsyuk in this case).

For Datsyuk he had a CorF% of 0.597 and a TMCorF% of 0.522. Zetterberg had a CorF% of 0.573 and a TMCorF% of 0.530. Differences in QoC are negligible (QoC is vastly over emphasized IMO) so one could rate Datsyuk's impact on his team as 0.597/0.522 or 1.14 and Zetterberg's impact as 0.573/0.530 or 1.08.

Datsyuk's 1.14 and Zetterberg's 1.08 could be considered their possession ratings relative to their teammates. These numbers are essentially a composite WOWY comparison. Doing this for all Red Wing forwards (with >750 minutes of 5v5 ZS adjusted ice time) we get:

Datsyuk 1.144 Zetterberg 1.081 Franzen 1.078 Hudler 1.030 Cleary 0.993 Miller 0.983 Abdelkader 0.983 Bertuzzi 0.951 Holmstrom 0.934 Filppula 0.897

To me I think those seem reasonable. The next step would be to merge them with team possession numbers to be able to compare them with the rest of the league. Simply multiplying by Team CorF% would probably do.

The Canucks forwards get ranked as follows:

Booth 1.122 D. Sedin 1.119 Kesler 1.107 H. Sedin 1.081 Higgins 1.060 Burrows 1.058 Hansen 0.987 Pahlsson 0.982 Raymond 0.933 Lapierre 0.901 Malhotra 0.790

There is probably a case study to be done with Malhotra because his possession numbers were horrible last season when he has generally been pretty good. Probably a significant part of it is his zone starts that aren't getting properly adjusted for in my zone start adjustment but even so, his down year last year was pretty extreme.

Thoughts?

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#13 Daniel Wagner
July 19 2012, 05:10AM
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Jared Lunsford wrote:

I'm not quite following you here. It seems to me that if you are comparing a good player on a good team to a good player on a bad team using Corsi Rel and believe this to be more accurate then you are using it to account for teammates.

I don't think I was quite clear and I admit to being somewhat at a loss when it comes to the finer intricacies of statistical analysis (I was in the Humanities, dammit!).

The more I look at what I wrote, the more I realize it doesn't actually make sense. By using Corsi Rel to compare players from different teams, I effectively am using Corsi Rel to account for teammates. It made so much more sense at the time: I blame lack of sleep.

You mention zone-adjusted Corsi as being more useful than Corsi Rel. Is there a readily available source for a player's zone-adjusted Corsi?

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#14 AronV
July 19 2012, 12:27PM
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"So they each played roughly 3 games' worth of time apart."

By this measure they only played 21 games together.

It's more like 9 games worth apart if you account for 20 minute games.

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#15 dan
July 19 2012, 08:52PM
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One correction: Weber and Suter's 'time apart' ~200 minutes. This equates to ~ 8 or 9 games (not 3 as you suggested) using ~18 19 min 5 on 5 even strength as an average.

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#16 dan
July 19 2012, 08:57PM
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@David Johnson

I have come up with a new adjustment for ozone starts (it falls between yours and D. Zona's and G. Ays). when I did them for the Canucks Maholtra came out very strong @ 55% adj. Pos F -checking back on his career in SJS this is not out of his range.Put me on the side that feels he is undervalued. Link to work here: http://www.nucksmisconduct.com/2012/6/6/3059415/review-scoring-chances

Coincidentally the Sedins and Burrows did not come out as strong.

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